In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations. 相似文献
This article concerns the analysis of an unsteady stagnation point flow of Eyring-Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme. A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme (RK-4) is available to show the credibility of the Galerkin method. The numerical exploration is carried out for various governing parameters, namely, Brownian motion, steadiness, thermophoresis, stretching ratio, velocity slip, concentration slip, thermal slip, and fluid parameters, and Hartmann, Prandtl and Schmidt numbers. The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing, but the behavior is reversed for assisting cases. The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases (assisting and opposing). The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter. All the outcomes and the behavior of emerging parameters are illustrated graphically. The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method. It is concluded that said method could be extended to other problems of a complex nature. 相似文献
This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package. 相似文献
Fractional pyrolysis and one-step pyrolysis of natural algae Cyanobacteria from Taihu Lake were comparatively studied from 200 to 500 ℃. One-step pyrolysis produced bio-oil with complex composition and low high heating value (HHV〈30.9 MJ/kg). Fractional pyrolysis separated the degradation of different components in Cyanobacteria and improved the selectivity to products in bio-oil. That is, acids at 200 ℃, amides and acids at 300 ℃, phenols and nitriles at 400 ℃, and phenols at 500 ℃, were got as main products, respectively. HZSM-5 could promote the dehydration, cracking and aromatization of pyrolytic intermediates in fractional pyrolysis. At optimal HZSM-5 catalyst dosage of 1.0 g, the selectivity to products and the quality of bio-oil were improved obviously. The main products in bio-oil changed to nitriles (47.2%) at 300 ℃, indoles (51.3%) and phenols (36.3%) at 400 ℃. The oxygen content was reduced to 7.2 wt% and 9.4 wt%, and the HHV was raised to 38.1 and 37.3 MJ/kg at 300 and 400 ℃, respectively. Fractional catalytic pyrolysis was proposed to be an efficient method not only to provide a potential solution for alleviating environmental pressure from water blooms, but also to improve the selectivity to products and obtain high quality bio-oil. 相似文献
The LB-DF/FD method derived from the Lattice Boltzmann Method and direct forcing/fictitious domain method is used to numerically investigate the dynamics and interaction of two elliptical particles settling in an infinitely long channel. One particle (EP0) is initially kept horizontal (major axis perpendicular to sedimentation) for all simulations while the other's (EP1) orientation is varied. It is found that if EP1strays away from horizontality, the particles undergo transitions from a steady state to reach a chaotic state. Furthermore, there are two distinct chaotic states for the particle motion when EP1 orientation is varied, in which a turning point is observed to distinguish the two states. 相似文献
The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional second-grade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semi-analytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.